Let's start by drawing a diagram corresponding to the situation. Notice that the sushi roll can be modeled by a circle, with the chopsticks being .

The diameter of the circle is then $3.5$ cm, the length of arc $BC$ is $4.7$ cm, and we are interested in the measure of angle $\angle A.$ To find this, we'll first need the $BC,$ which we can find by the . The circumference is
$\pi d = \pi \cdot 3.5 \approx 11.0 \text{ cm.}$
We can now calculate the arc measure.

$\dfrac{\text{arc length}}{\text{circumference}} = \dfrac{\text{arc measure}}{360^\circ}$

$\dfrac{{\color{#0000FF}{4.7}}}{{\color{#009600}{11.0}}} = \dfrac{\text{arc measure}}{360^\circ}$

$\dfrac{4.7}{11.0} \cdot 360^\circ = \text{arc measure}$

$153.81818\ldots^\circ = \text{arc measure}$

$154^\circ \approx \text{arc measure}$

$\text{arc measure} \approx 154^\circ$

We now know that the measure of arc $BC$ is $154^\circ.$ As $ABOC$ is a quadrilateral, it has the interior angle sum $360^\circ.$ With $m\angle B$ and $m\angle C$ being $90^\circ,$ the sum of $m\angle A$ and $m\angle O$ must then be $180^\circ.$

$m\angle A + m\angle O = 180^\circ$

$m\angle A + 154^\circ = 180^\circ$

$m\angle A = 26^\circ$

The measure of the circumscribed angle is $26^\circ.$